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| {{About|velocity in physics}}
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| {{refimprove|date=March 2011}}
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| {{Infobox physical quantity
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| |bgcolour={default}
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| |name = Velocity
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| |image= [[File:US Navy 040501-N-1336S-037 The U.S. Navy sponsored Chevy Monte Carlo NASCAR leads a pack into turn four at California Speedway.jpg|260px]]
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| |caption= As a change of direction occurs while the cars turn on the curved track, their velocity is not constant.
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| |unit = [[meter|m]]/[[second|s]]
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| |symbols = ''v'', '''v'''
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| }}
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| {{Classical mechanics|cTopic=Fundamental concepts}}
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| '''Velocity''' is the [[Time derivative|rate of change]] of the [[Position (vector)|position]] of an object, equivalent to a specification of its [[speed]] and direction of motion, e.g. 60 km/h to the north.
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| Velocity is an important concept in [[kinematics]], the branch of [[classical mechanics]] which describes the [[motion (physics)|motion]] of bodies.
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| Velocity is a [[vector (geometry)|vector]] [[physical quantity]]; both magnitude and direction are required to define it. The [[scalar (physics)|scalar]] [[absolute value]] ([[Magnitude (mathematics)|magnitude]]) of velocity is called "speed", a quantity that is measured in [[metres per second]] (m/s or m·s<sup>−1</sup>) in the [[International System of Units|SI]] (metric) system. For example, "5 metres per second" is a [[Scalar (physics)|scalar]] (not a vector), whereas "5 metres per second east" is a vector.
| | It involves expertise and knowledge of various tools and technologies used for creating websites. It is thus, on these grounds that compel various web service provider companies to integrate the same in their packages too. Your parishioners and certainly interested audience can come in to you for further information from the group and sometimes even approaching happenings and systems with the church. They found out all the possible information about bringing up your baby and save money at the same time. You can easily customize the titles of the posts in Word - Press blog in a way that only title comes in the new post link and not the date or category of posts. <br><br>Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. But in case you want some theme or plugin in sync with your business needs, it is advisable that you must seek some professional help. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. As of now, Pin2Press is getting ready to hit the market. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. If you loved this article in addition to you would like to be given more info relating to [http://mmservice.dk/wordpress_backup_393615 wordpress dropbox backup] kindly pay a visit to our own webpage. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. After that the developer adds the unordered list for navigations. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. * Robust CRM to control and connect with your subscribers. When we talk about functional suitability, Word - Press proves itself as one of the strongest contestant among its other rivals. If you are looking for Hire Wordpress Developer then just get in touch with him. Look for experience: When you are searching for a Word - Press developer you should always look at their experience level. <br><br>There is no denying that Magento is an ideal platform for building ecommerce websites, as it comes with an astounding number of options that can help your online business do extremely well. An ease of use which pertains to both internet site back-end and front-end users alike. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. Thus, Word - Press is a good alternative if you are looking for free blogging software. For your information, it is an open source web content management system. |
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| If there is a change in speed, direction, or both, then the object has a changing velocity and is said to be undergoing an ''[[acceleration]]''.
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| ==Constant velocity vs acceleration==
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| To have a '''constant velocity''', an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path (the object's path does not curve). Thus, a constant velocity means motion in a straight line at a constant speed.
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| <!-- Could discuss the basic equations of motion of a body moving at constant velocity here. -->
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| For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.
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| ==Distinction between speed and velocity==
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| [[Speed]] describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving.<ref>{{cite book|last=Wilson|first=Edwin Bidwell|title=Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs|year=1901|pages=125|url=http://hdl.handle.net/2027/mdp.39015000962285?urlappend=%3Bseq=149}} This is the likely origin of the speed/velocity terminology in vector physics.</ref> If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.
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| The big difference can be noticed when we consider movement around a circle. When something moves in a circle and returns to its starting point its average velocity is zero but its average [[speed]] is found by dividing the [[circumference]] of the [[circle]] by the time taken to move around the [[circle]]. This is because the average velocity is calculated by only considering the [[Displacement (vector)|displacement]] between the starting and the end points while the average speed considers only the total [[distance]] traveled.
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| ==Equation of motion==
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| {{main|Equation of motion}}
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| The ''average'' velocity <math>\boldsymbol{\bar{v}}</math> of an object moving through a [[displacement (vector)|displacement]] <math>( \Delta \boldsymbol{x})</math> during a time interval <math>( \Delta t)</math> is described by the formula:
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| :<math>\boldsymbol{\bar{v}} = \frac{\Delta \boldsymbol{x}}{\Delta t}.</math>
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| The velocity vector '''''v''''' of an object that has positions <math>x(t)</math> at time <math>t</math> and <math>x(t + \Delta t)</math> at time <math>t + \Delta t</math>, can be computed as the [[derivative]] of position:
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| :<math>\boldsymbol{v} = \lim_{\Delta t \to 0}{{\boldsymbol{x}(t+\Delta t)-\boldsymbol{x}(t)} \over \Delta t}={\mathrm{d} \boldsymbol{x} \over \mathrm{d}t}.</math>
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| More simply, for motion in one dimension, velocity can be defined as the slope of the [[Position (vector)|position]] vs. time graph of an object.
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| Average velocity magnitudes are always smaller than or equal to average speed of a given particle.
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| Instantaneous velocity is always tangential to trajectory.
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| Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity.
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| The equation for an object's velocity can be obtained mathematically by evaluating the [[integral]] of the equation for its acceleration beginning from some initial period time <math>t_0</math> to some point in time later <math>t_n</math>. | |
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| The final velocity '''''v''''' of an object which starts with velocity '''''u''''' and then accelerates at constant acceleration '''''a''''' for a period of time <math>\Delta t</math> is:
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| :<math>\boldsymbol{v} = \boldsymbol{u} + \boldsymbol{a} \Delta t. </math>
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| The average velocity of an object undergoing constant [[acceleration]] is <math>\tfrac {(\boldsymbol{u} + \boldsymbol{v})}{2}</math>, where '''''u''''' is the initial velocity and '''''v''''' is the final velocity. To find the position, '''''x''''', of such an accelerating object during a time interval, <math>\Delta t</math>, then:
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| :<math> \Delta \boldsymbol{x} = \frac {( \boldsymbol{u} + \boldsymbol{v} )}{2}\Delta t.</math>
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| When only the object's initial velocity is known, the expression,
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| :<math> \Delta \boldsymbol{x} = \boldsymbol{u} \Delta t + \frac{1}{2}\boldsymbol{a} \Delta t^2,</math>
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| can be used.
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| This can be expanded to give the position at any time ''t'' in the following way:
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| :<math> \boldsymbol{x}(t) = \boldsymbol{x}(0) + \Delta \boldsymbol{x} = \boldsymbol{x}(0) + \boldsymbol{u} \Delta t + \frac{1}{2}\boldsymbol{a} \Delta t^2,</math>
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| These basic equations for final velocity and position can be combined to form an equation that is independent of time, also known as [[Torricelli's equation]]:
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| :<math>v^2 = u^2 + 2a\Delta x.\,</math>
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| The above equations are valid for both [[Classical mechanics|Newtonian mechanics]] and [[special relativity]]. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian mechanics, all observers agree on the value of ''t'' and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words only relative velocity can be calculated.
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| In Newtonian mechanics, the [[kinetic energy]] ([[energy]] of motion), <math>E_K</math>, of a moving object is linear with both its [[mass]] and the square of its velocity:
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| :<math>E_{K} = \begin{matrix} \frac{1}{2} \end{matrix} m \boldsymbol{v}^2.</math>
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| The kinetic energy is a [[scalar (physics)|scalar]] quantity. | |
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| ''[[Escape velocity]]'' is the minimum a [[ballistic]] object needs to escape from a massive body like the earth. It represents the kinetic energy that when added to the object's [[gravitational potential energy]] (which is always negative) is greater than or equal to zero. Escape velocity from the Earth's surface is about 11 100 m/s.
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| ==Relative velocity==
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| {{main|Relative velocity}}
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| '''Relative velocity''' is a measurement of velocity between two objects
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| as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with [[special relativity]] in which velocities depend on the choice of reference frame.
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| If an object A is moving with velocity [[vector (geometry)|vector]] '''''v''''' and an object B with velocity vector '''''w''''', then the velocity of object A ''relative to'' object B is defined as the difference of the two velocity vectors:
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| :<math>\boldsymbol{v}_{A\text{ relative to }B} = \boldsymbol{v} - \boldsymbol{w}</math>
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| Similarly the relative velocity of object B moving with velocity '''''w''''', relative to object A moving with velocity '''''v''''' is:
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| :<math>\boldsymbol{v}_{B\text{ relative to }A} = \boldsymbol{w} - \boldsymbol{v}</math>
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| Usually the inertial frame is chosen in which the latter of the two mentioned objects is in rest.
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| ===Scalar velocities===
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| In the one dimensional case,<ref>[http://www.saburchill.com/physics/chapters/0083.html Basic principle]</ref> the velocities are scalars and the equation is either:
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| :<math>\, v_{rel} = v - (-w)</math>, if the two objects are moving in opposite directions, or:
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| :<math>\, v_{rel} = v -(+w)</math>, if the two objects are moving in the same direction.
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| ==Polar coordinates==<!-- This section is linked from [[Doppler effect]] -->
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| In [[Polar coordinate system|polar coordinates]], a two-dimensional velocity is described by a [[radial velocity]], defined as the component of velocity away from or toward the origin (also known as ''velocity made good''), and an [[angular velocity]], which is the rate of rotation about the origin (with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system). | |
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| The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The [[Transversality (mathematics)|transverse]] velocity is the component of velocity along a circle centered at the origin.
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| :<math>\boldsymbol{v}=\boldsymbol{v}_T+\boldsymbol{v}_R</math>
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| where
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| :<math>\boldsymbol{v}_T</math> is the transverse velocity
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| :<math>\boldsymbol{v}_R</math> is the radial velocity.
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| The ''magnitude of the radial velocity'' is the [[dot product]] of the velocity vector and the unit vector in the direction of the displacement. | |
| :<math>v_R=\frac{\boldsymbol{v} \cdot \boldsymbol{r}}{\left|\boldsymbol{r}\right|}</math>
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| where
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| :<math>\boldsymbol{r}</math> is displacement.
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| The ''magnitude of the transverse velocity'' is that of the [[cross product]] of the unit vector in the direction of the displacement and the velocity vector. It is also the product of the [[angular speed]] <math>\omega</math> and the magnitude of the displacement.
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| :<math>v_T=\frac{|\boldsymbol{r}\times\boldsymbol{v}|}{|\boldsymbol{r}|}=\omega|\boldsymbol{r}|</math>
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| such that
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| :<math>\omega=\frac{|\boldsymbol{r}\times\boldsymbol{v}|}{|\boldsymbol{r}|^2}.</math>
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| [[Angular momentum]] in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity.
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| :<math>L=mrv_T=mr^2\omega\,</math>
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| where
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| :<math>m\,</math> is mass
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| :<math>r=\|\boldsymbol{r}\|.</math>
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| The expression <math>mr^2</math> is known as [[moment of inertia]].
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| If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational [[orbit]], angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as [[Kepler's laws of planetary motion]].
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| ==See also==
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| {{cmn|2|
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| *[[Four-velocity]] (relativistic version of velocity for [[Minkowski spacetime]])
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| *[[Group velocity]]
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| *[[Hypervelocity]]
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| *[[Phase velocity]]
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| *[[Proper velocity]] (in relativity, using traveler time instead of observer time)
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| *[[Rapidity]] (a version of velocity additive at relativistic speeds)
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| *[[Terminal velocity]]
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| *[[Velocity vs. time graph]]
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| }}
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| ==Notes==
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| {{reflist|2}}
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| ==References==
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| * Robert Resnick and Jearl Walker, ''Fundamentals of Physics'', Wiley; 7 Sub edition (June 16, 2004). ISBN 0-471-23231-9.
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| ==External links==
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| {{commons category}}
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| *[http://www.physicsclassroom.com/Class/1DKin/U1L1d.html Physicsclassroom.com], Speed and Velocity
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| *[http://www.scs.cmu.edu/~rapidproto/mechanisms/chpt1.html Introduction to Mechanisms] ([[Carnegie Mellon University]])
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| {{Kinematics}}
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| [[Category:Motion]]
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| [[Category:Kinematics]]
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| [[Category:Velocity| ]]
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| [[Category:Concepts in physics]]
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| [[fr:Vecteur vitesse]]
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| [[hy:Արագություն]]
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